Prime number 31 can be expressed in the form n^5 -1, where n=2. Are there any other primes that can be expressed this way?
No other primes can be expressed as n^5-1
n^5-1 is divisible by n-1 as per below formula. So for any value of n>2 the resulting number will be a composite number. a^5 – b^5 = (a – b)(a^4 + a^3*b + a^2*b^2 + a*b^3 + b^4)
31 = [2^5 - 1] is a Mersenne Prime. The next in the list is [2^7 - 1] = [128 - 1] = 127 [2^77232917 - 1] is the largest Mersenne Prime as of last year.
If 1/x - 1/y = - 29 and the value of (x +12xy - y) / (x - 6xy -y) can be expressed as m/n, where m and n are co prime positive integers. The value of m + n = ?
Four different prime numbers 5, 7, 17 and 19 such that the sum of any three of them is also a prime. Are there 5 different positive primes such that the sum of any three of them is also a prime?
There are 168 primes less than 1,000. What is the sum of the prime numbers less than 1,000?
(a) 11,555 (b) 76,127 (c) 57,298 (d) 81,722
Find the largest possible value of positive integer N, such that N! can be expressed as the product of (N-4) consecutive positive integers?
